# @version ^0.2.8
"""
@title StableSwap
@author Curve.Fi
@license Copyright (c) Curve.Fi, 2020 - all rights reserved
@notice Pool implementation with aToken-style lending
@dev This contract is only a template, pool-specific constants
     must be set prior to compiling. Note that this template is
     currently compatible with aTokens (Aave) and that for other
     protocols selected parts in the code may need to be changed.
"""

from vyper.interfaces import ERC20


interface LendingPool:
    def withdraw(_underlying_asset: address, _amount: uint256, _receiver: address): nonpayable

interface CurveToken:
    def totalSupply() -> uint256: view
    def mint(_to: address, _value: uint256) -> bool: nonpayable
    def burnFrom(_to: address, _value: uint256) -> bool: nonpayable


# Events
event TokenExchange:
    buyer: indexed(address)
    sold_id: int128
    tokens_sold: uint256
    bought_id: int128
    tokens_bought: uint256

event TokenExchangeUnderlying:
    buyer: indexed(address)
    sold_id: int128
    tokens_sold: uint256
    bought_id: int128
    tokens_bought: uint256

event AddLiquidity:
    provider: indexed(address)
    token_amounts: uint256[N_COINS]
    fees: uint256[N_COINS]
    invariant: uint256
    token_supply: uint256

event RemoveLiquidity:
    provider: indexed(address)
    token_amounts: uint256[N_COINS]
    fees: uint256[N_COINS]
    token_supply: uint256

event RemoveLiquidityOne:
    provider: indexed(address)
    token_amount: uint256
    coin_amount: uint256

event RemoveLiquidityImbalance:
    provider: indexed(address)
    token_amounts: uint256[N_COINS]
    fees: uint256[N_COINS]
    invariant: uint256
    token_supply: uint256

event CommitNewAdmin:
    deadline: indexed(uint256)
    admin: indexed(address)

event NewAdmin:
    admin: indexed(address)

event CommitNewFee:
    deadline: indexed(uint256)
    fee: uint256
    admin_fee: uint256
    offpeg_fee_multiplier: uint256

event NewFee:
    fee: uint256
    admin_fee: uint256
    offpeg_fee_multiplier: uint256

event RampA:
    old_A: uint256
    new_A: uint256
    initial_time: uint256
    future_time: uint256

event StopRampA:
    A: uint256
    t: uint256


# These constants must be set prior to compiling
N_COINS: constant(int128) = ___N_COINS___
PRECISION_MUL: constant(uint256[N_COINS]) = ___PRECISION_MUL___

# fixed constants
FEE_DENOMINATOR: constant(uint256) = 10 ** 10
PRECISION: constant(uint256) = 10 ** 18  # The precision to convert to

MAX_ADMIN_FEE: constant(uint256) = 10 * 10 ** 9
MAX_FEE: constant(uint256) = 5 * 10 ** 9

MAX_A: constant(uint256) = 10 ** 6
MAX_A_CHANGE: constant(uint256) = 10
A_PRECISION: constant(uint256) = 100

ADMIN_ACTIONS_DELAY: constant(uint256) = 3 * 86400
MIN_RAMP_TIME: constant(uint256) = 86400

coins: public(address[N_COINS])
underlying_coins: public(address[N_COINS])
admin_balances: public(uint256[N_COINS])

fee: public(uint256)  # fee * 1e10
offpeg_fee_multiplier: public(uint256)  # * 1e10
admin_fee: public(uint256)  # admin_fee * 1e10

owner: public(address)
lp_token: public(address)

# This may need to be changed for non-aave pools! 
aave_lending_pool: address
aave_referral: uint256

initial_A: public(uint256)
future_A: public(uint256)
initial_A_time: public(uint256)
future_A_time: public(uint256)

admin_actions_deadline: public(uint256)
transfer_ownership_deadline: public(uint256)
future_fee: public(uint256)
future_admin_fee: public(uint256)
future_offpeg_fee_multiplier: public(uint256)  # * 1e10
future_owner: public(address)

is_killed: bool
kill_deadline: uint256
KILL_DEADLINE_DT: constant(uint256) = 2 * 30 * 86400


@external
def __init__(
    _coins: address[N_COINS],
    _underlying_coins: address[N_COINS],
    _pool_token: address,
    _aave_lending_pool: address,
    _A: uint256,
    _fee: uint256,
    _admin_fee: uint256,
    _offpeg_fee_multiplier: uint256,
):
    """
    @notice Contract constructor
    @param _coins List of wrapped coin addresses
    @param _underlying_coins List of underlying coin addresses
    @param _pool_token Pool LP token address
    @param _aave_lending_pool Aave lending pool address
    @param _A Amplification coefficient multiplied by n * (n - 1)
    @param _fee Swap fee expressed as an integer with 1e10 precision
    @param _admin_fee Percentage of fee taken as an admin fee,
                      expressed as an integer with 1e10 precision
    @param _offpeg_fee_multiplier Offpeg fee multiplier
    """
    for i in range(N_COINS):
        assert _coins[i] != ZERO_ADDRESS
        assert _underlying_coins[i] != ZERO_ADDRESS
    self.coins = _coins
    self.underlying_coins = _underlying_coins
    self.initial_A = _A * A_PRECISION
    self.future_A = _A * A_PRECISION
    self.fee = _fee
    self.admin_fee = _admin_fee
    self.offpeg_fee_multiplier = _offpeg_fee_multiplier
    self.owner = msg.sender
    self.kill_deadline = block.timestamp + KILL_DEADLINE_DT
    self.lp_token = _pool_token
    self.aave_lending_pool = _aave_lending_pool

    # approve transfer of underlying coin to aave lending pool
    for coin in _underlying_coins:
        _response: Bytes[32] = raw_call(
            coin,
            concat(
                method_id("approve(address,uint256)"),
                convert(_aave_lending_pool, bytes32),
                convert(MAX_UINT256, bytes32)
            ),
            max_outsize=32
        )
        if len(_response) != 0:
            assert convert(_response, bool)


@view
@internal
def _A() -> uint256:
    """
    Handle ramping A up or down
    """
    t1: uint256 = self.future_A_time
    A1: uint256 = self.future_A

    if block.timestamp < t1:
        A0: uint256 = self.initial_A
        t0: uint256 = self.initial_A_time
        # Expressions in uint256 cannot have negative numbers, thus "if"
        if A1 > A0:
            return A0 + (A1 - A0) * (block.timestamp - t0) / (t1 - t0)
        else:
            return A0 - (A0 - A1) * (block.timestamp - t0) / (t1 - t0)

    else:  # when t1 == 0 or block.timestamp >= t1
        return A1


@view
@external
def A() -> uint256:
    return self._A() / A_PRECISION


@view
@external
def A_precise() -> uint256:
    return self._A()


@pure
@internal
def _dynamic_fee(_xpi: uint256, _xpj: uint256, _fee: uint256, _feemul: uint256) -> uint256:
    if _feemul <= FEE_DENOMINATOR:
        return _fee
    else:
        xps2: uint256 = (_xpi + _xpj)
        xps2 *= xps2  # Doing just ** 2 can overflow apparently
        return (_feemul * _fee) / (
            (_feemul - FEE_DENOMINATOR) * 4 * _xpi * _xpj / xps2 + \
            FEE_DENOMINATOR)


@view
@external
def dynamic_fee(i: int128, j: int128) -> uint256:
    """
    @notice Return the fee for swapping between `i` and `j`
    @param i Index value for the coin to send
    @param j Index value of the coin to recieve
    @return Swap fee expressed as an integer with 1e10 precision
    """
    precisions: uint256[N_COINS] = PRECISION_MUL
    xpi: uint256 = (ERC20(self.coins[i]).balanceOf(self) - self.admin_balances[i]) * precisions[i]
    xpj: uint256 = (ERC20(self.coins[j]).balanceOf(self) - self.admin_balances[j]) * precisions[j]
    return self._dynamic_fee(xpi, xpj, self.fee, self.offpeg_fee_multiplier)


@view
@external
def balances(i: uint256) -> uint256:
    """
    @notice Get the current balance of a coin within the
            pool, less the accrued admin fees
    @param i Index value for the coin to query balance of
    @return Token balance
    """
    return ERC20(self.coins[i]).balanceOf(self) - self.admin_balances[i]


@view
@internal
def _balances() -> uint256[N_COINS]:
    result: uint256[N_COINS] = empty(uint256[N_COINS])
    for i in range(N_COINS):
        result[i] = ERC20(self.coins[i]).balanceOf(self) - self.admin_balances[i]
    return result


@pure
@internal
def _get_D(_xp: uint256[N_COINS], _amp: uint256) -> uint256:
    """
    D invariant calculation in non-overflowing integer operations
    iteratively

    A * sum(x_i) * n**n + D = A * D * n**n + D**(n+1) / (n**n * prod(x_i))

    Converging solution:
    D[j+1] = (A * n**n * sum(x_i) - D[j]**(n+1) / (n**n prod(x_i))) / (A * n**n - 1)
    """
    S: uint256 = 0
    Dprev: uint256 = 0

    for _x in _xp:
        S += _x
    if S == 0:
        return 0

    D: uint256 = S
    Ann: uint256 = _amp * N_COINS
    for _i in range(255):
        D_P: uint256 = D
        for _x in _xp:
            D_P = D_P * D / (_x * N_COINS)  # If division by 0, this will be borked: only withdrawal will work. And that is good
        Dprev = D
        D = (Ann * S / A_PRECISION + D_P * N_COINS) * D / ((Ann - A_PRECISION) * D / A_PRECISION + (N_COINS + 1) * D_P)
        # Equality with the precision of 1
        if D > Dprev:
            if D - Dprev <= 1:
                return D
        else:
            if Dprev - D <= 1:
                return D
    # convergence typically occurs in 4 rounds or less, this should be unreachable!
    # if it does happen the pool is borked and LPs can withdraw via `remove_liquidity`
    raise



@view
@internal
def _get_D_precisions(_coin_balances: uint256[N_COINS], _amp: uint256) -> uint256:
    xp: uint256[N_COINS] = PRECISION_MUL
    for i in range(N_COINS):
        xp[i] *= _coin_balances[i]
    return self._get_D(xp, _amp)


@view
@external
def get_virtual_price() -> uint256:
    """
    @notice The current virtual price of the pool LP token
    @dev Useful for calculating profits
    @return LP token virtual price normalized to 1e18
    """
    D: uint256 = self._get_D_precisions(self._balances(), self._A())
    # D is in the units similar to DAI (e.g. converted to precision 1e18)
    # When balanced, D = n * x_u - total virtual value of the portfolio
    token_supply: uint256 = ERC20(self.lp_token).totalSupply()
    return D * PRECISION / token_supply


@view
@external
def calc_token_amount(_amounts: uint256[N_COINS], _is_deposit: bool) -> uint256:
    """
    @notice Calculate addition or reduction in token supply from a deposit or withdrawal
    @dev This calculation accounts for slippage, but not fees.
         Needed to prevent front-running, not for precise calculations!
    @param _amounts Amount of each coin being deposited
    @param _is_deposit set True for deposits, False for withdrawals
    @return Expected amount of LP tokens received
    """
    amp: uint256 = self._A()
    coin_balances: uint256[N_COINS] = self._balances()
    D0: uint256 = self._get_D_precisions(coin_balances, amp)
    for i in range(N_COINS):
        if _is_deposit:
            coin_balances[i] += _amounts[i]
        else:
            coin_balances[i] -= _amounts[i]
    D1: uint256 = self._get_D_precisions(coin_balances, amp)
    token_amount: uint256 = CurveToken(self.lp_token).totalSupply()
    diff: uint256 = 0
    if _is_deposit:
        diff = D1 - D0
    else:
        diff = D0 - D1
    return diff * token_amount / D0


@external
@nonreentrant('lock')
def add_liquidity(_amounts: uint256[N_COINS], _min_mint_amount: uint256, _use_underlying: bool = False) -> uint256:
    """
    @notice Deposit coins into the pool
    @param _amounts List of amounts of coins to deposit
    @param _min_mint_amount Minimum amount of LP tokens to mint from the deposit
    @param _use_underlying If True, deposit underlying assets instead of aTokens
    @return Amount of LP tokens received by depositing
    """
    assert not self.is_killed  # dev: is killed

    amp: uint256 = self._A()
    old_balances: uint256[N_COINS] = self._balances()
    
    # Initial invariant
    D0: uint256 = self._get_D_precisions(old_balances, amp)
    
    lp_token: address = self.lp_token
    token_supply: uint256 = CurveToken(lp_token).totalSupply()
    new_balances: uint256[N_COINS] = old_balances
    for i in range(N_COINS):
        if token_supply == 0:
            assert _amounts[i] > 0  # dev: initial deposit requires all coins
        new_balances[i] += _amounts[i]

    # Invariant after change
    D1: uint256 = self._get_D_precisions(new_balances, amp)
    assert D1 > D0

    # We need to recalculate the invariant accounting for fees
    # to calculate fair user's share
    fees: uint256[N_COINS] = empty(uint256[N_COINS])
    mint_amount: uint256 = 0
    if token_supply > 0:
        # Only account for fees if we are not the first to deposit
        ys: uint256 = (D0 + D1) / N_COINS
        fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))
        feemul: uint256 = self.offpeg_fee_multiplier
        admin_fee: uint256 = self.admin_fee
        for i in range(N_COINS):
            ideal_balance: uint256 = D1 * old_balances[i] / D0
            difference: uint256 = 0
            new_balance: uint256 = new_balances[i]
            if ideal_balance > new_balance:
                difference = ideal_balance - new_balance
            else:
                difference = new_balance - ideal_balance
            xs: uint256 = old_balances[i] + new_balance
            fees[i] = self._dynamic_fee(xs, ys, fee, feemul) * difference / FEE_DENOMINATOR
            if admin_fee != 0:
                self.admin_balances[i] += fees[i] * admin_fee / FEE_DENOMINATOR
            new_balances[i] = new_balance - fees[i]
        D2: uint256 = self._get_D_precisions(new_balances, amp)
        mint_amount = token_supply * (D2 - D0) / D0
    else:
        mint_amount = D1  # Take the dust if there was any

    assert mint_amount >= _min_mint_amount, "Slippage screwed you"

    # Take coins from the sender
    if _use_underlying:
        lending_pool: address = self.aave_lending_pool
        # This may not be needed for non-aave pools
        aave_referral: bytes32 = convert(self.aave_referral, bytes32)

        # Take coins from the sender
        for i in range(N_COINS):
            amount: uint256 = _amounts[i]
            if amount != 0:
                coin: address = self.underlying_coins[i]
                # transfer underlying coin from msg.sender to self
                _response: Bytes[32] = raw_call(
                    coin,
                    concat(
                        method_id("transferFrom(address,address,uint256)"),
                        convert(msg.sender, bytes32),
                        convert(self, bytes32),
                        convert(amount, bytes32)
                    ),
                    max_outsize=32
                )
                if len(_response) > 0:
                    assert convert(_response, bool)

                # deposit to aave lending pool: this may need to be changed for non-aave pools!
                raw_call(
                    lending_pool,
                    concat(
                        method_id("deposit(address,uint256,address,uint16)"),
                        convert(coin, bytes32),
                        convert(amount, bytes32),
                        convert(self, bytes32),
                        aave_referral,
                    )
                )
    else:
        for i in range(N_COINS):
            amount: uint256 = _amounts[i]
            if amount != 0:
                _response: Bytes[32] = raw_call(
                    self.coins[i],
                    concat(
                        method_id("transferFrom(address,address,uint256)"),
                        convert(msg.sender, bytes32),
                        convert(self, bytes32),
                        convert(amount, bytes32)
                    ),
                    max_outsize=32
                )
                if len(_response) > 0:
                    assert convert(_response, bool)
    # Mint pool tokens
    CurveToken(lp_token).mint(msg.sender, mint_amount)

    log AddLiquidity(msg.sender, _amounts, fees, D1, token_supply + mint_amount)

    return mint_amount


@view
@internal
def _get_y(i: int128, j: int128, x: uint256, _xp: uint256[N_COINS]) -> uint256:
    """
    Calculate x[j] if one makes x[i] = x

    Done by solving quadratic equation iteratively.
    x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)
    x_1**2 + b*x_1 = c

    x_1 = (x_1**2 + c) / (2*x_1 + b)
    """
    # x in the input is converted to the same price/precision

    assert i != j       # dev: same coin
    assert j >= 0       # dev: j below zero
    assert j < N_COINS  # dev: j above N_COINS

    # should be unreachable, but good for safety
    assert i >= 0
    assert i < N_COINS

    A: uint256 = self._A()
    D: uint256 = self._get_D(_xp, A)
    Ann: uint256 = A * N_COINS
    c: uint256 = D
    S: uint256 = 0
    _x: uint256 = 0
    y_prev: uint256 = 0

    for _i in range(N_COINS):
        if _i == i:
            _x = x
        elif _i != j:
            _x = _xp[_i]
        else:
            continue
        S += _x
        c = c * D / (_x * N_COINS)
    c = c * D * A_PRECISION / (Ann * N_COINS)
    b: uint256 = S + D * A_PRECISION / Ann  # - D
    y: uint256 = D
    for _i in range(255):
        y_prev = y
        y = (y*y + c) / (2 * y + b - D)
        # Equality with the precision of 1
        if y > y_prev:
            if y - y_prev <= 1:
                return y
        else:
            if y_prev - y <= 1:
                return y
    raise


@view
@internal
def _get_dy(i: int128, j: int128, _dx: uint256) -> uint256:
    xp: uint256[N_COINS] = self._balances()
    precisions: uint256[N_COINS] = PRECISION_MUL
    for k in range(N_COINS):
        xp[k] *= precisions[k]

    x: uint256 = xp[i] + _dx * precisions[i]
    y: uint256 = self._get_y(i, j, x, xp)
    dy: uint256 = (xp[j] - y) / precisions[j]
    fee: uint256 = self._dynamic_fee(
            (xp[i] + x) / 2, (xp[j] + y) / 2, self.fee, self.offpeg_fee_multiplier
        ) * dy / FEE_DENOMINATOR
    return dy - fee


@view
@external
def get_dy(i: int128, j: int128, _dx: uint256) -> uint256:
    return self._get_dy(i, j, _dx)


@view
@external
def get_dy_underlying(i: int128, j: int128, _dx: uint256) -> uint256:
    return self._get_dy(i, j, _dx)


@internal
def _exchange(i: int128, j: int128, dx: uint256) -> uint256:
    assert not self.is_killed  # dev: is killed
    # dx and dy are in aTokens

    xp: uint256[N_COINS] = self._balances()
    precisions: uint256[N_COINS] = PRECISION_MUL
    for k in range(N_COINS):
        xp[k] *= precisions[k]

    x: uint256 = xp[i] + dx * precisions[i]
    y: uint256 = self._get_y(i, j, x, xp)
    dy: uint256 = xp[j] - y
    dy_fee: uint256 = dy * self._dynamic_fee(
            (xp[i] + x) / 2, (xp[j] + y) / 2, self.fee, self.offpeg_fee_multiplier
        ) / FEE_DENOMINATOR

    admin_fee: uint256 = self.admin_fee
    if admin_fee != 0:
        dy_admin_fee: uint256 = dy_fee * admin_fee / FEE_DENOMINATOR
        if dy_admin_fee != 0:
            self.admin_balances[j] += dy_admin_fee / precisions[j]

    return (dy - dy_fee) / precisions[j]


@external
@nonreentrant('lock')
def exchange(i: int128, j: int128, _dx: uint256, _min_dy: uint256) -> uint256:
    """
    @notice Perform an exchange between two coins
    @dev Index values can be found via the `coins` public getter method
    @param i Index value for the coin to send
    @param j Index valie of the coin to recieve
    @param _dx Amount of `i` being exchanged
    @param _min_dy Minimum amount of `j` to receive
    @return Actual amount of `j` received
    """
    dy: uint256 = self._exchange(i, j, _dx)
    assert dy >= _min_dy, "Exchange resulted in fewer coins than expected"

    _response: Bytes[32] = raw_call(
        self.coins[i],
        concat(
            method_id("transferFrom(address,address,uint256)"),
            convert(msg.sender, bytes32),
            convert(self, bytes32),
            convert(_dx, bytes32),
        ),
        max_outsize=32,
    )
    if len(_response) > 0:
        assert convert(_response, bool)

    _response = raw_call(
        self.coins[j],
        concat(
            method_id("transfer(address,uint256)"),
            convert(msg.sender, bytes32),
            convert(dy, bytes32),
        ),
        max_outsize=32,
    )
    if len(_response) > 0:
        assert convert(_response, bool)

    log TokenExchange(msg.sender, i, _dx, j, dy)

    return dy


@external
@nonreentrant('lock')
def exchange_underlying(i: int128, j: int128, _dx: uint256, _min_dy: uint256) -> uint256:
    """
    @notice Perform an exchange between two underlying coins
    @dev Index values can be found via the `underlying_coins` public getter method
    @param i Index value for the underlying coin to send
    @param j Index valie of the underlying coin to recieve
    @param _dx Amount of `i` being exchanged
    @param _min_dy Minimum amount of `j` to receive
    @return Actual amount of `j` received
    """
    dy: uint256 = self._exchange(i, j, _dx)
    assert dy >= _min_dy, "Exchange resulted in fewer coins than expected"

    u_coin_i: address = self.underlying_coins[i]
    lending_pool: address = self.aave_lending_pool

    # transfer underlying coin from msg.sender to self
    _response: Bytes[32] = raw_call(
        u_coin_i,
        concat(
            method_id("transferFrom(address,address,uint256)"),
            convert(msg.sender, bytes32),
            convert(self, bytes32),
            convert(_dx, bytes32)
        ),
        max_outsize=32,
    )
    if len(_response) > 0:
        assert convert(_response, bool)

    # deposit to aave lending pool: this may need to be changed for non-aave pools!
    raw_call(
        lending_pool,
        concat(
            method_id("deposit(address,uint256,address,uint16)"),
            convert(u_coin_i, bytes32),
            convert(_dx, bytes32),
            convert(self, bytes32),
            convert(self.aave_referral, bytes32),
        )
    )
    # withdraw `j` underlying from lending pool and transfer to caller
    LendingPool(lending_pool).withdraw(self.underlying_coins[j], dy, msg.sender)

    log TokenExchangeUnderlying(msg.sender, i, _dx, j, dy)

    return dy


@external
@nonreentrant('lock')
def remove_liquidity(
    _amount: uint256,
    _min_amounts: uint256[N_COINS],
    _use_underlying: bool = False,
) -> uint256[N_COINS]:
    """
    @notice Withdraw coins from the pool
    @dev Withdrawal amounts are based on current deposit ratios
    @param _amount Quantity of LP tokens to burn in the withdrawal
    @param _min_amounts Minimum amounts of underlying coins to receive
    @param _use_underlying If True, withdraw underlying assets instead of aTokens
    @return List of amounts of coins that were withdrawn
    """
    amounts: uint256[N_COINS] = self._balances()
    lp_token: address = self.lp_token
    total_supply: uint256 = CurveToken(lp_token).totalSupply()

    lending_pool: address = ZERO_ADDRESS
    if _use_underlying:
        lending_pool = self.aave_lending_pool

    for i in range(N_COINS):
        value: uint256 = amounts[i] * _amount / total_supply
        assert value >= _min_amounts[i], "Withdrawal resulted in fewer coins than expected"
        amounts[i] = value
        if _use_underlying:
            LendingPool(lending_pool).withdraw(self.underlying_coins[i], value, msg.sender)
        else:
            _response: Bytes[32] = raw_call(
                self.coins[i],
                concat(
                    method_id("transfer(address,uint256)"),
                    convert(msg.sender, bytes32),
                    convert(value, bytes32),
                ),
                max_outsize=32,
            )
            if len(_response) > 0:
                assert convert(_response, bool)
    
    CurveToken(lp_token).burnFrom(msg.sender, _amount)  # dev: insufficient funds
    log RemoveLiquidity(msg.sender, amounts, empty(uint256[N_COINS]), total_supply - _amount)

    return amounts


@external
@nonreentrant('lock')
def remove_liquidity_imbalance(
    _amounts: uint256[N_COINS],
    _max_burn_amount: uint256,
    _use_underlying: bool = False
) -> uint256:
    """
    @notice Withdraw coins from the pool in an imbalanced amount
    @param _amounts List of amounts of underlying coins to withdraw
    @param _max_burn_amount Maximum amount of LP token to burn in the withdrawal
    @param _use_underlying If True, withdraw underlying assets instead of aTokens
    @return Actual amount of the LP token burned in the withdrawal
    """
    assert not self.is_killed  # dev: is killed

    amp: uint256 = self._A()
    old_balances: uint256[N_COINS] = self._balances()
    D0: uint256 = self._get_D_precisions(old_balances, amp)
    new_balances: uint256[N_COINS] = old_balances
    for i in range(N_COINS):
        new_balances[i] -= _amounts[i]
    D1: uint256 = self._get_D_precisions(new_balances, amp)
    ys: uint256 = (D0 + D1) / N_COINS
    fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))
    feemul: uint256 = self.offpeg_fee_multiplier
    admin_fee: uint256 = self.admin_fee
    fees: uint256[N_COINS] = empty(uint256[N_COINS])
    for i in range(N_COINS):
        ideal_balance: uint256 = D1 * old_balances[i] / D0
        new_balance: uint256 = new_balances[i]
        difference: uint256 = 0
        if ideal_balance > new_balance:
            difference = ideal_balance - new_balance
        else:
            difference = new_balance - ideal_balance
        xs: uint256 = new_balance + old_balances[i]
        fees[i] = self._dynamic_fee(xs, ys, fee, feemul) * difference / FEE_DENOMINATOR
        if admin_fee != 0:
            self.admin_balances[i] += fees[i] * admin_fee / FEE_DENOMINATOR
        new_balances[i] -= fees[i]
    D2: uint256 = self._get_D_precisions(new_balances, amp)

    lp_token: address = self.lp_token
    token_supply: uint256 = CurveToken(lp_token).totalSupply()
    token_amount: uint256 = (D0 - D2) * token_supply / D0
    assert token_amount != 0  # dev: zero tokens burned
    assert token_amount <= _max_burn_amount, "Slippage screwed you"

    CurveToken(lp_token).burnFrom(msg.sender, token_amount)  # dev: insufficient funds

    lending_pool: address = ZERO_ADDRESS
    if _use_underlying:
        lending_pool = self.aave_lending_pool

    for i in range(N_COINS):
        amount: uint256 = _amounts[i]
        if amount != 0:
            if _use_underlying:
                LendingPool(lending_pool).withdraw(self.underlying_coins[i], amount, msg.sender)
            else:
                _response: Bytes[32] = raw_call(
                self.coins[i],
                concat(
                    method_id("transfer(address,uint256)"),
                    convert(msg.sender, bytes32),
                    convert(amount, bytes32),
                ),
                max_outsize=32,
                )
                if len(_response) > 0:
                    assert convert(_response, bool)

    log RemoveLiquidityImbalance(msg.sender, _amounts, fees, D1, token_supply - token_amount)

    return token_amount


@pure
@internal
def _get_y_D(A: uint256, i: int128, _xp: uint256[N_COINS], D: uint256) -> uint256:
    """
    Calculate x[i] if one reduces D from being calculated for xp to D

    Done by solving quadratic equation iteratively.
    x_1**2 + x_1 * (sum' - (A*n**n - 1) * D / (A * n**n)) = D ** (n + 1) / (n ** (2 * n) * prod' * A)
    x_1**2 + b*x_1 = c

    x_1 = (x_1**2 + c) / (2*x_1 + b)
    """
    # x in the input is converted to the same price/precision

    assert i >= 0  # dev: i below zero
    assert i < N_COINS  # dev: i above N_COINS

    Ann: uint256 = A * N_COINS
    c: uint256 = D
    S: uint256 = 0
    _x: uint256 = 0
    y_prev: uint256 = 0

    for _i in range(N_COINS):
        if _i != i:
            _x = _xp[_i]
        else:
            continue
        S += _x
        c = c * D / (_x * N_COINS)
    c = c * D * A_PRECISION / (Ann * N_COINS)
    b: uint256 = S + D * A_PRECISION / Ann
    y: uint256 = D

    for _i in range(255):
        y_prev = y
        y = (y*y + c) / (2 * y + b - D)
        # Equality with the precision of 1
        if y > y_prev:
            if y - y_prev <= 1:
                return y
        else:
            if y_prev - y <= 1:
                return y
    raise


@view
@internal
def _calc_withdraw_one_coin(_token_amount: uint256, i: int128) -> uint256:
    # First, need to calculate
    # * Get current D
    # * Solve Eqn against y_i for D - _token_amount
    amp: uint256 = self._A()
    xp: uint256[N_COINS] = self._balances()
    precisions: uint256[N_COINS] = PRECISION_MUL

    for j in range(N_COINS):
        xp[j] *= precisions[j]

    D0: uint256 = self._get_D(xp, amp)
    D1: uint256 = D0 - _token_amount * D0 / ERC20(self.lp_token).totalSupply()
    new_y: uint256 = self._get_y_D(amp, i, xp, D1)

    xp_reduced: uint256[N_COINS] = xp
    ys: uint256 = (D0 + D1) / (2 * N_COINS)

    fee: uint256 = self.fee * N_COINS / (4 * (N_COINS - 1))
    feemul: uint256 = self.offpeg_fee_multiplier
    for j in range(N_COINS):
        dx_expected: uint256 = 0
        xavg: uint256 = 0
        if j == i:
            dx_expected = xp[j] * D1 / D0 - new_y
            xavg = (xp[j] + new_y) / 2
        else:
            dx_expected = xp[j] - xp[j] * D1 / D0
            xavg = xp[j]
        xp_reduced[j] -= self._dynamic_fee(xavg, ys, fee, feemul) * dx_expected / FEE_DENOMINATOR

    dy: uint256 = xp_reduced[i] - self._get_y_D(amp, i, xp_reduced, D1)

    return (dy - 1) / precisions[i]


@view
@external
def calc_withdraw_one_coin(_token_amount: uint256, i: int128) -> uint256:
    """
    @notice Calculate the amount received when withdrawing a single coin
    @dev Result is the same for underlying or wrapped asset withdrawals
    @param _token_amount Amount of LP tokens to burn in the withdrawal
    @param i Index value of the coin to withdraw
    @return Amount of coin received
    """
    return self._calc_withdraw_one_coin(_token_amount, i)


@external
@nonreentrant('lock')
def remove_liquidity_one_coin(
    _token_amount: uint256,
    i: int128,
    _min_amount: uint256,
    _use_underlying: bool = False
) -> uint256:
    """
    @notice Withdraw a single coin from the pool
    @param _token_amount Amount of LP tokens to burn in the withdrawal
    @param i Index value of the coin to withdraw
    @param _min_amount Minimum amount of coin to receive
    @param _use_underlying If True, withdraw underlying assets instead of aTokens
    @return Amount of coin received
    """
    assert not self.is_killed  # dev: is killed

    dy: uint256 = self._calc_withdraw_one_coin(_token_amount, i)
    assert dy >= _min_amount, "Not enough coins removed"

    CurveToken(self.lp_token).burnFrom(msg.sender, _token_amount)  # dev: insufficient funds

    if _use_underlying:
        LendingPool(self.aave_lending_pool).withdraw(self.underlying_coins[i], dy, msg.sender)
    else:
        _response: Bytes[32] = raw_call(
        self.coins[i],
        concat(
            method_id("transfer(address,uint256)"),
            convert(msg.sender, bytes32),
            convert(dy, bytes32),
        ),
        max_outsize=32,
        )
        if len(_response) > 0:
            assert convert(_response, bool)

    log RemoveLiquidityOne(msg.sender, _token_amount, dy)

    return dy


### Admin functions ###

@external
def ramp_A(_future_A: uint256, _future_time: uint256):
    assert msg.sender == self.owner  # dev: only owner
    assert block.timestamp >= self.initial_A_time + MIN_RAMP_TIME
    assert _future_time >= block.timestamp + MIN_RAMP_TIME  # dev: insufficient time

    initial_A: uint256 = self._A()
    future_A_p: uint256 = _future_A * A_PRECISION

    assert _future_A > 0 and _future_A < MAX_A
    if future_A_p < initial_A:
        assert future_A_p * MAX_A_CHANGE >= initial_A
    else:
        assert future_A_p <= initial_A * MAX_A_CHANGE

    self.initial_A = initial_A
    self.future_A = future_A_p
    self.initial_A_time = block.timestamp
    self.future_A_time = _future_time

    log RampA(initial_A, future_A_p, block.timestamp, _future_time)


@external
def stop_ramp_A():
    assert msg.sender == self.owner  # dev: only owner

    current_A: uint256 = self._A()
    self.initial_A = current_A
    self.future_A = current_A
    self.initial_A_time = block.timestamp
    self.future_A_time = block.timestamp
    # now (block.timestamp < t1) is always False, so we return saved A

    log StopRampA(current_A, block.timestamp)


@external
def commit_new_fee(_new_fee: uint256, _new_admin_fee: uint256, _new_offpeg_fee_multiplier: uint256):
    assert msg.sender == self.owner  # dev: only owner
    assert self.admin_actions_deadline == 0  # dev: active action
    assert _new_fee <= MAX_FEE  # dev: fee exceeds maximum
    assert _new_admin_fee <= MAX_ADMIN_FEE  # dev: admin fee exceeds maximum
    assert _new_offpeg_fee_multiplier * _new_fee <= MAX_FEE * FEE_DENOMINATOR  # dev: offpeg multiplier exceeds maximum

    deadline: uint256 = block.timestamp + ADMIN_ACTIONS_DELAY
    self.admin_actions_deadline = deadline
    self.future_fee = _new_fee
    self.future_admin_fee = _new_admin_fee
    self.future_offpeg_fee_multiplier = _new_offpeg_fee_multiplier

    log CommitNewFee(deadline, _new_fee, _new_admin_fee, _new_offpeg_fee_multiplier)


@external
def apply_new_fee():
    assert msg.sender == self.owner  # dev: only owner
    assert block.timestamp >= self.admin_actions_deadline  # dev: insufficient time
    assert self.admin_actions_deadline != 0  # dev: no active action

    self.admin_actions_deadline = 0
    fee: uint256 = self.future_fee
    admin_fee: uint256 = self.future_admin_fee
    fml: uint256 = self.future_offpeg_fee_multiplier
    self.fee = fee
    self.admin_fee = admin_fee
    self.offpeg_fee_multiplier = fml

    log NewFee(fee, admin_fee, fml)


@external
def revert_new_parameters():
    assert msg.sender == self.owner  # dev: only owner

    self.admin_actions_deadline = 0


@external
def commit_transfer_ownership(_owner: address):
    assert msg.sender == self.owner  # dev: only owner
    assert self.transfer_ownership_deadline == 0  # dev: active transfer

    deadline: uint256 = block.timestamp + ADMIN_ACTIONS_DELAY
    self.transfer_ownership_deadline = deadline
    self.future_owner = _owner

    log CommitNewAdmin(deadline, _owner)


@external
def apply_transfer_ownership():
    assert msg.sender == self.owner  # dev: only owner
    assert block.timestamp >= self.transfer_ownership_deadline  # dev: insufficient time
    assert self.transfer_ownership_deadline != 0  # dev: no active transfer

    self.transfer_ownership_deadline = 0
    owner: address = self.future_owner
    self.owner = owner

    log NewAdmin(owner)


@external
def revert_transfer_ownership():
    assert msg.sender == self.owner  # dev: only owner

    self.transfer_ownership_deadline = 0


@external
def withdraw_admin_fees():
    assert msg.sender == self.owner  # dev: only owner

    for i in range(N_COINS):
        value: uint256 = self.admin_balances[i]
        if value > 0:
            _response: Bytes[32] = raw_call(
                self.coins[i],
                concat(
                    method_id("transfer(address,uint256)"),
                    convert(msg.sender, bytes32),
                    convert(value, bytes32),
                ),
                max_outsize=32,
            )  # dev: failed transfer
            if len(_response) > 0:
                assert convert(_response, bool)
            self.admin_balances[i] = 0


@external
def donate_admin_fees():
    """
    Just in case admin balances somehow become higher than total (rounding error?)
    this can be used to fix the state, too
    """
    assert msg.sender == self.owner  # dev: only owner
    self.admin_balances = empty(uint256[N_COINS])


@external
def kill_me():
    assert msg.sender == self.owner  # dev: only owner
    assert self.kill_deadline > block.timestamp  # dev: deadline has passed
    self.is_killed = True


@external
def unkill_me():
    assert msg.sender == self.owner  # dev: only owner
    self.is_killed = False


@external
def set_aave_referral(_referral_code: uint256):  # This may not be required for non-aave pools
    assert msg.sender == self.owner  # dev: only owner
    assert _referral_code < 2 ** 16  # dev: uint16 overflow
    self.aave_referral = _referral_code